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Crank
3 years ago
8

Using the formula for volume of a cone, express r in terms of V, h and pi

Mathematics
2 answers:
Ne4ueva [31]3 years ago
8 0

Answer:

r = \sqrt{\displaystyle\frac{3V}{h\pi}}

Step-by-step explanation:

We are given the following information in the question.

Using the formula for volume of cone, we have to express r in terms of V, h and pi.

Formula:

\text{Volume of cone, V} = \displaystyle\frac{1}{3}\pi r^2 h\\\\\text{where r is the radius of cone, h is the height of radius}

Now, we have to evaluate r, the radius of cone.

Rearranging the terms, we have,

Working:

V = \displaystyle\frac{1}{3}\pi r^2 h\\\\r^2 = \frac{3\times V}{\pi\times h}\\\\r^2 = \frac{3V}{h\pi}\\\\r = \sqrt{\frac{3V}{h\pi}}.

Thus, r in form of V, h and pi can be written as:

r = \sqrt{\displaystyle\frac{3V}{h\pi}}

DiKsa [7]3 years ago
3 0

The volume of the cone is one-third of the volume of the cylinder which is equal to the product of area of the base and the height. The equation is,

<span>    V = (1/3)(pi)(r^2)h          </span>

Dividing both sides of the equation by (1/3)(pi)(h) will give us,

<span>  3V/(pi)(h) = r^2</span>

Taking the square-root of both sides,

<span>  r = sqrt(3V/(pi)(h))</span>

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